Kubelka-Munk theory is oftentimes used to analyze the diffuse reflective spectra from a coating on a target surface. The use of the two-flux approximation Kubelka Munk equations for color-matching a coating on the target surface generally requires two primary assumptions. First, the refractive index of the sample being measured is the same as the refractive index of air. To correct the refractive index assumption, the Saunderson correction equation is employed. The Saunderson correction equation employs the use of two Fresnel coefficients, K1 and K2, which take into account the refractive index of the coated surface in question. As used herein, the K1 coefficient represents the fractional reflectance when light entering the target sample is partially reflected at the sample surface and the K2 coefficient represents the fractional reflectance when light exiting the sample is partially reflected back into the sample at the sample surface. The second assumption is that 100% of the incident light on the coated surface is either absorbed or scattered by the coating in a uniform manner, leaving no edge effects. This assumption further results in the expectation of a linear relationship between K (absorption) and S (scattering), “K/S”, of the pigment over the concentration range of that pigment's usage and that the relationship will be the same across all viewing angles.
The two-flux approximation Kubelka-Munk equations are sufficient for characterization of solid, opaque dispersed pigmentations coated to opacity. However, with the introduction and subsequent rise in desirability and popularity of gonioapparent special effect pigments and highly transparent dispersed pigments and dyes, the two-flux approximation Kubelka-Munk theory breaks down.
In order to account for the aforementioned new pigment types and technologies, a pseudo-multiflux approach can be employed. Historically and in theory, the multiflux approach has been to allow the K2 Fresnel coefficient in the Saunderson equation, which converts measured reflectance to internal reflectance, to vary dependent on wavelength. Also, the variation of the K1 Fresnel coefficient by wavelength has been employed as well.
Thus, there is a need for a system and process that varies the K1 and K2 Fresnel coefficients by wavelength, angle and concentration such that the K1 and K2 values become functions of concentration, given a particular angle and wavelength combination.